The scientific aim of the space gravitational-wave (GW) detector Laser Interferometer Space Antenna (LISA) that was scheduled to launch in the early 2030s is to detect the low-frequency GW signals in the Galaxy. Its main candidate GW sources are compact binaries of white dwarfs and neutron stars. In this work, we examine whether compact intermediate-mass black hole (IMBH) X-ray binaries could be potential LISA sources. Our simulations indicate that an IMBH binary with a 1000 M IMBH and a 3 M donor star in an initial orbital period near the so-called bifurcation period of 0.77 day could evolve into an ultra-compact X-ray binary, which will emit GW signals with a maximum frequency of 2.5 mHz. According to the evolutionary tracks of characteristic strain, IMBH X-ray binaries with the initial donor-star masses of 1-3 M and the initial orbital periods slightly less than the bifurcation periods will be detectable by the LISA in a distance of 15 kpc. Assuming each of 60 Galactic globular clusters hosts a 1000 M IMBH, the maximum number of compact IMBH X-ray binaries that LISA will detect in the Galaxy should be less than ten. Therefore, the detectability of compact IMBH X-ray binaries by the LISA is not optimistic.